I'm pretty biased about him, but I think Jose Ferrer manages to make it work, no matter what. Of course, that isn't really answering your question about the whole episode.
I agree with Grant that Jose Ferrer's presence is strong, and I even think the little kid is a pretty good actor (for a kid); it impresses me how this youngster seems so relaxed and natural in a cast otherwise dominated by actors over forty (and a dog and robot). I'm also quite fond of the ending when Columbo pretends to arrest Ferrer's son; one of the more intense culminations to a case. I agree, though, that there is a sort of campy feel to the episode. Even the title of the film Steve Spelberg laments he's too young to see sounds incredibly campy (of course, that's probably the point in that case).
I don't think this episode is as bad as is sometimes made out. Actually, the first half hour is pretty good. The motive is interesting and has something in common with 'A Stitch in Time' - it's a shame this wasn't explored further. Also a shame that the victim couldn't have survived a little longer, as he seemed a much more credible character than some of the others. The supporting cast is a bit weak I think.
I can't help disagreeing about the supporting cast. Obviously Ferrer "carries" the story, and not just by playing the killer, but it does have several good actors in it. I've always thought of Robert Walker Jr. as a very underrated actor, either from "living in the shadow" of his father or whatever other reason, and I think he's good in this.
I couldn't get over the idea that the writers expected us to ignore the fact that the institute was in the traitorous business of grooming foreign military leaders on warfare tactics like a perfectly legitimate exercise of genius, but that ridiculousness aside, that Cahill's reason for murdering Nicholson was as incredibly lame as his way of going about it.
It was definitely better than I remembered. I enjoyed watching Columbo in this one, not a bad episode. I over looked the robot and just payed attention to Columbo solving the murder. It was better than Most Dangerous Match.
So were Margret and Neil really having an affair? Was the hotel guy a plant?
Only reason I can imagine was to settle his nerves. My ex-editor always had to step outside for a cig when he was agitated (usually after conversations with me, alas). Nonetheless enjoyed the ep for Ferrer's performance and the weird atmosphere (one of the reasons I liked Bye-Bye et al Murder Case -- it played like some strange little Kafka-esque stage play).